Accelerating Real-Time Coupled Cluster Methods with Single-Precision Arithmetic and Adaptive Numerical Integration

TL;DR

This paper presents a method to accelerate real-time coupled cluster calculations by using single-precision arithmetic, GPU implementation, and adaptive numerical integration, achieving significant speedups without compromising accuracy.

Contribution

It introduces a combined approach of single-precision arithmetic, GPU acceleration, and adaptive integration algorithms to enhance the efficiency of real-time coupled cluster simulations.

Findings

Single-precision reduces storage and computation costs by about half.

GPU implementation speeds up simulations by up to 14 times.

Adaptive integrators balance computational cost and numerical stability.

Abstract

We explore the framework of a real-time coupled cluster method with a focus on improving its computational efficiency. Propagation of the wave function via the time-dependent Schr\"odinger equation places high demands on computing resources, particularly for high level theories such as coupled cluster with polynomial scaling. Similar to earlier investigations of coupled cluster properties, we demonstrate that the use of single-precision arithmetic reduces both the storage and multiplicative costs of the real-time simulation by approximately a factor of two with no significant impact on the resulting UV/vis absorption spectrum computed via the Fourier transform of the time-dependent dipole moment. Additional speedups of up to a factor of 14 in test simulations of water clusters are obtained via a straightforward GPU-based implementation as compared to conventional CPU calculations. We also find that further performance optimization is accessible through sagacious selection of numerical integration algorithms, and the adaptive methods, such as the Cash-Karp integrator provide an effective balance between computing costs and numerical stability. Finally, we demonstrate that a simple mixed-step integrator based on the conventional fourth-order Runge-Kutta approach is capable of stable propagations even for strong external fields, provided the time step is appropriately adapted to the duration of the laser pulse with only minimal computational overhead.